Mapping degrees of complexity, complicatedness

Mapping degrees of complexity, complicatedness, and emergent complexity Timothy F.H. Allena , Preston Austinb , Mario Giampietroc,d , Zora Kovacicd, *, Edmond Ramlye , Joseph Tainterf a

University of Wisconsin-Madison, Birge Hall, 430 Lincoln Dr, Madison, WI 53706, United States

b

Rabble, 7 North Pinckney St, Madison, WI 53703, United States

c

ICREA, Passeig Lluis Companys 23, 08010 Barcelona, Spain

d

Institut de Ciencia i Tecnologia Ambientals, Universitat Autonoma de Barcelona, Edifici Z, Campus UAB, 08193 Bellaterra, Cerdanyola del Valles, Spain e

Center for Health Systems Research and Analysis, College of Engineering, University of WisconsinMadison,610 Walnut Street, Madison, WI 53726-2397, United States f

Department of Environment and Society, Utah State University, Logan, UT 84321, United States

1. Introduction This paper limits itself to epistemology and remains agnostic as to ontology, which is a separate discourse. Our only reference to ontology is to specify how the epistemology of a situation is separate from ontology, and cannot be directly linked. Ontology is a separate discourse that needs its own terms beyond the scope of the present paper. We work hard to show how epistemology is of limited utility in the realm of ontological assertions. In ecology, ontology is too often used as a direct lever in epistemological discourse. The eminent organismal ecologist, Dick Tracy, once said to Allen that ecosystems and communities are abstractions, but he studies organisms, and at least they are real. Allen even checked back years later, and Tracy confirmed his sentiments. Many would agree with his assertion, but we would not. For us neither ecosystems nor organisms are real independent of abstraction. One of our aims is to sort out the muddles that can occur when epistemological arguments are used to justify directly ontological beliefs. There are good reasons for the tradition of philosophers in keeping epistemology separate from ontology. Even so, ecologists are often willing to rely on what they suppose is the real situation to clench their arguments, particularly with regard to the complexity of an ecological situation. Our concern for complexity carries our epistemological arguments. Ecologists are challenged by distinctions between complexity and simplicity, and between complexity and complication. Complexity swirls around the interface between materiality and abstractions. Materiality is external to the observer while abstraction is created by human observers. Complexity is one of those things that certainly feels real enough and material, while suggesting one cannot quite put their finger on it. Ecologists know complexity when they see it, while sometimes not being able to define it confidently. Some will vehemently insist that complexity is a reflection of materiality in a way that is real; something that is so self-evident it must have a material basis. Others, like us, are much more skeptical. In this paper we refer to Rosen’s work on complexity to come down on one side or the other for the origins of complexity. Rosen starts his discussion of complexity from the basic duality between the self and everything else (1991). One can experience the self, but everything else, or what Rosen calls the “external world” (1991: 41), is not directly accessible. According to Rosen, one’s understanding of the external world is based on modelling. Modelling consists of establishing congruence between one’s

entailment system and the external world. Entailment invokes a loop of logical consistency surrounding the model, “if, if, if, then.” Rosen invokes a causal loop of entailment in the functioning of the observed. He works with observables not reality. A modelling relation is established when “we have brought at least a part of the inferential machinery . . . into congruence with a corresponding part of the [observed system]” (1991: 54). Complexity arises when a system does not match the predictions of the formal model used to describe it. A simple system is one that can be correctly predicted by a model. A complex system is one which cannot be fully simulated, or computed, using models. In Rosen’s words, a complex system “must have a nonsimulable model” (Rosen, 2000: 292). Complexity would “require, at best, an infinite number of distinct formalizations to capture all the qualities” (Rosen, 1991: 9) missed by the entailment system of computable models. Complexity is thus a relational property, derived from the comparison between the observed system and its model. Rosennean complexity is an epistemological issue, not a property of the external world. Nevertheless, complexity has material consequences. In his study of complex societies, Tainter argues that complexity is used as a problem-solving strategy, so that societies evolve from less to more complex. The purpose of this paper is to assess the implications of Rosennean complexity for ecology, and for the study of complex systems. First, we assess the implications of Rosen’s epistemological definition of complexity with respect to material difference. The possibility of the materiality of complexity stands as the basis of the analysis of complex systems, a central concept in ecology. Second, we compare Rosen’s and Tainter’s assessment of complexity with regard to the concept of emergence and the possibility of degrees of complexity. Third, we distinguish between complexity and complicatedness to draw attention to the potentially confounding interaction between abstraction required to deal with the material world and the material world itself.

2. Material difference One way to narrow things down is to look at a simple system and, with all else equal, seek its complex counterpart, for comparison. As an explanatory example we use the conversion of a merely complicated version of an army on the move and compare that to its complex battle-ready condition. For our military example, Rick Atkinson (Atkinson, 1943) reports on the Allied Expeditionary Force in WWII in 1942 as it left North America sailing for North Africa near Casablanca. The ships were loaded with regard to sailing across the Atlantic. Batteries were loaded deep in the hold because they were heavy, so that they could serve as ballast. So the loading did have some order to it, but that had little to do with criteria for efficient unloading while facing resistance to the landing. The model for the simple system might take the form of the position of all the bits of materiel on the boats. Such a model is complicated but distinctly possible. There were many degrees of freedom as to where what military equipment was put on the ships. The functioning of the invading force as such was not much of a consideration, beyond having all the pertinent materiel on board somewhere. In a sense the loaded ships were largely unorganized. That would make the system only complicated; that is an elaborate version of simple, but still simple. Guns and ammunition were not loaded near each other, and gun sites were loaded somewhere else. Medical supplies, important as casualties mount in the beach landings, were not loaded so they could be readily unloaded early in disembarkation. To achieve invasion the materiel had to be organized. This amounted to converting a complicated only simple system into one that became complex. It took days for the gunners, the ammunition, the guns and the gun sites to be all in one place. Only over time did the complicated system of loaded boats become organized into a complex fighting system. The difference in this case was organization. Degrees of freedom were removed as the parts of functioning guns were constrained to be together in space. The organized invading force consisted of the same materiel, that is to say material, as the unorganized loaded boats. The difference is the

elaborate constraints on the parts for a challenging task. So while the constraints have material consequences as to space and material, the complexity is more conceptual and less physical. So complexity appears in a dance with the material system, but is not exactly material itself. The complicated and complex versions of the army consist of largely the same material parts, so no difference there. That denies most of the case for the difference between complicated and complex being directly material. Complexity in this case was achieved by organizing the parts in relation to each other, by imposing constraints and denying the parts degrees of freedom. In the historical army, that did move the material parts this way and that, but the complexity itself was embodied in a plan and its purpose, not material complexity, whatever that might be. That plan invokes Aristotle’s formal cause not his material cause. Complexity appears to relate to purpose and function. The purpose in question in the army example is clear, it is the purpose of battle, but sometimes it can be purpose coming from the observer understanding the situation. In an ecological example, that purpose may be something like the reason for leaves being flat to facilitate photosynthesis. The leaves are not sitting there scheming, and evolution did not aim; the purpose is found in the observer seeking an explanation for the form of foliage. Organization is focused so that complexity appears or disappears as the focus of the story-teller is changed. Notice that the batteries loaded as ballast is a matter of organization to a degree, just not the same degree as in the emergent complexity facilitating the invasion. Complexity emerges by crossing a threshold in the context of a function. Certainly some aspects of complexity appear quite concrete, but the hook is that the concrete arises only after some decision has been made or some situation is named and determined. The ease with which abstraction may be mistaken for something material can be shown by the concept of dominant and recessive genes. The error in understanding dominance as concrete is almost universal. Almost all biologists would come down on the material side for genetic dominance. Dominant genes have material consequences as a result of the mechanics of protein synthesis. Dominance is expressed as material observed characters in the organism which overcome any recessive character also in the genome. The gene codes for a protein, the consequence of which is a biochemical species that causes the dominant character to be expressed. Surely that makes dominant as opposed to recessive a material happening? Not so fast! Sickle cell anemia is caused by a mutation in the gene which codes for the structure of the protein hemoglobin. But if in the diploid genome the normal gene is also present, sickle cell pathology is not expressed because it is recessive. The reason for dominance is that only one dose of the normal hemoglobin gene needs to be present for normal hemoglobin to be the manifestation in the phenotype of the heterozygote. But the wrinkle is that the heterozygote in sickle cell shows resistance to malaria. That would make the sickle cell gene dominant for malarial resistance. But we never put it in such terms, because the sickle cell condition is at least deleterious, and often fatal. One might complain that we are raising an unusual somehow perverse case, but in fact we are only allowing the commonplace to be seen. The general condition is that all genes are dominant for the protein for which they code, and are recessive for all other proteins. There are physical consequences for a gene being dominant, but that does not make dominance itself a material matter. The physicality of a dominant gene arises only once human value judgements and abstractions have been chosen, and the protein is assessed as being significant. For instance, the normal gene for hemoglobin is in fact recessive for malarial resistance. To press the case that genetic dominance is not material, consider that genes that arise from mutation in a population are generally recessive. When over time such genes become advantageous they assume dominance, but with no material change in their structure or functioning. Simply, the character is seen in a differentlight, and that is a normative shift not one that is material. Advantageous genes become common in the population and are then

taken as the norm or the default against which dominance is assessed. The old dominant gene is still dominant for its own character, it is just that its character is no longer considered important enough to be part of what is considered dominant. It is still there but it does not matter. Dominant carries with it a value judgement of somehow normal, common, the default, or advantageous. The discussion here is not about dominance per se, but rather points at how much that is presumed to be material is not so. Alongside dominance, complexity also appears to have a material connection, without it actually being material. Like dominance, complexity is always set inside some chosen context that makes things seem complex. Another example of only apparent materiality has been highlighted by Tainter and Lucas (Tainter and Lucas, 1983). They point out that significance in an archeological site is not material. An insignificant site with no pot chards can later become significant when techniques for carbon dating and interpretation of charred grain fragments become available. The site has become significant with no change in the material present. What has changed is the meaning of some material, and that is not itself material.

3. Emergence Complexity is a matter of emergence (Rosen, 1991). Emergence too sits astride materiality and human decisions. Often with emergence there is some new configuration, as when a gradient of water over a hole causes the emergence of a whirlpool. Emergence does not have to occur over time, it can appear with a change in decisions as to the span of the universe under consideration. The new configuration may have its novelty in a widening of the discourse, such as widening the universe from that with room for only a single proton to one big enough to include two atoms. Atthat point there can be chemistry as an emergent, which it is impossible to be seen in a single proton. In emergence of a whirlpool the flow of water also needs to be recognized as a gyre that is judged different from just gurgling down the hole. As an emergent property the gyre must be distinguished from the previous glug-glug–glug of the flow of water that was not a whirlpool. Both gurgles and whirlpools represent the passage of water, so it is possible not to notice the change. So emergence is the recognition of a physical change, not just the physical change. In emergence an old constraint is broken. Often the cause of breakdown of an old regime appears as a naked positive feedback which just runs. In the end it finds itself up against a negative feedback or a constraint. There is an emergence manifested in the new constraint. Emergence is not just the breaking loose of an old constraint, it is the order that comes with being pressed up against the new constraint. Emergence is a constraint manifesting itself. Rosen is concerned with complexity that has to do with coupling a formal representation to meaning. Rosennean complexity indicates representation referring to “emergence." It is important to flag that not only the observer matters but also the interpreter who asks why you are describing the system. In the flat leaf example the interpreter suggests that leaves are a funny shape, and that requires an explanation. As explained by Rosen: a rock can be simple for someone kicking it while walking or complex for a geologist studying the characteristics of a site. So complexity à la Rosen is an all or nothing effect, with no degree of complexity, just an instance of it. If the information can be handled by a computer without the need for using semantics, then it is simple. Alternatively, if one needs a semantic process to handle the meaning of the formal representation it is complex. Tainter draws attention to problem solving by societies that find solutions in increasing complexity. He is often less concerned than Rosen as to the particular threshold crossed in achieving complexity. For Tainter there is complexity as he begins his discussion, and it often increases in societies over time. This might easily be misconstrued as being in conflict with Rosen’s discourse. All or nothing would appear to be at odds degrees of increasing complexity, but it is not because the character of the discourse is different, and it is at a different level of analysis. The new

constraint that increases in Tainter’s complex societies will have some design to it. The degrees of complexity to which Tainter refers do not focus on the observation-observer complex, but on the goals. This invokes definitions of relevance of the storyteller, the one deciding why to describe the system. Thus Rosen and Tainter refer to complexity following different agendas, but each agenda does not make the respective other agenda wrong. The use of constraints is nuanced. In an emerging system before it hits the constraint a positive feedback is not ordered because it is unconstrained. Positive feedback is pure dynamics with no definable structure. Designed complexification can be seen as an analogy to moving up steps. In Fig. 1 the vertical part of the step is the disordered situation before constraints impose order. Up against the constraint is the flat constrained part of the step, a manifestation of complexity. In human societies there will be other constraints that are not part of achieving a step up. An example might be the number of farmers in 1300 AD England, constrained by availability of land. The English farmers’ constraints are not necessarily part of an ordered increase in complexity. Complexity depends on constraints, but particular constraints may or may not contribute to complexity. In the step up, the vertical part of the step is unconstrained with respect to some old broken constraint; the new higher level has not yet manifested itself in emergence. Disorder can sometimes be seen relative to some increase in order, such as the coming of industrial production. By contrast the constraints on English farmers in 1300 AD need not be seen as constraining societal order. The step up and the ordering constraint in that vicinity might be constraints in the Industrial Revolution. In Fig. 1 that constrained situation would be the ordered step up. Increasing trade probably is part of the emergence of industrial society. Rosen contrasts complexity with simplicity, implying that complexity is all or nothing. And in his narrow universes of discourse he is right. There is complexity or not, which would appear to deny degrees of complexity. Inside local universes Rosen’s implications hold (Table 1). For Rosen the universal relationship is between particular simplicity from which a particular complexity emerged. Rosen’s all-or-nothing being said, it is still possible for the emergence of different complex structures to occur in a sequential fashion of increasing complexity in a wider universe B. The order of the steps comes from imposing new constraints on top of old extant constraints. This allows the notion of human society increasing in complexity in the last 10,000 years. Without an ordered context within which comparison can be made, different versions of complexity are just different, not ordered in increasing or decreasing complexity; there is no way to compare simply different versions of complexity. Comparison requires a common context, like Rome for the Roman Republic and the Roman Empire. When Tainter considers societies emerging, he sees them complexifying to solve problems. The same society at some later time may add complexity to solve successive problems. It is a general property of complex human societies. His central thesis for collapse of complex societies (Tainter, 1988) is that the very process of problem solving fails as complexification appears not to be worth it. There will be some disruptive event, but that is not the cause of collapse. His argument is that, with too much complexity, if not this event causing collapse then it would have been another. The reason for collapse is the process of diminishing returns on effort with problem solving. The complexification is in the end not worth the effort, and problem-solving itself fails. Collapsing and complexifying human society is a logical type (Whitehead and Russell, 1910, 1912, 1913) and that allows degrees of complexity. A logical type is a discourse with a specific degree of equivalence within. Dog and cat belong to a particular logical type, characterized as a diverse set of lines of evolution within the mammalian order Carnivora. Carnivore is in a different logical type from dog, although it is related. Another member of the carnivore logical type is herbivore. The logical type is ‘animal defined by what it eats.’ Being a carnivore does not amount to dog and cat, but can be a category to which dog and cat belong. So within the wide discourse surrounding

human societies there is room for degrees of complexity in the examples. The degree is within the larger logical type, which allows comparison of the various complexities involved. Thus Rosen and Tainter’s views of complexity can be compatible, albeit about difference facets of complexity. All this is consistent with Fig. 1, which shows thresholds for complexity. It allows for the coexistence of increasing ordered complexity over the steps, as well as the Rosennean complexity which is the emergence of a particular step as an instance of complex emergence. There are two “as opposed to whats.” One is the distinction between the previous simple below the step (that is Rosen). The second is a complexity all in the same general discourse; steps can be compared, and later steps are more complex (this is Tainter). All scientific statements are as opposed to what. Put all the complexity and simplicity together, and then we get the general confused muddle that surrounds complexity in principle.

4. Complication Complexity has a set of issues that appear variously related, sometimes appearing at odds with each other. A larger discourse can lead to consonance. Some of these issues turn on differences in definitions, but others require a more nuanced analysis under the same definition. One area of concern asks whether complexity is material or is an abstraction. There is often a general confusion that complexity is material. It may pertain to material situations, but that does not make complexity itself material. That line of argument appears difficult for realists, and may be one of the good reasons for adopting postmodernity. Another topic probes the distinction between complicatedness and complexity. We gave the example of the complicated Allied Invasion Force in North Africa. The army was forced into becoming complex for it to follow its final Aristotelian cause (Ulanowicz, 1997) as a whole entity. Some of the confusion surrounding the materiality of complexity may come from the lack of a distinction between complex and complicated. Complicatedness still involves human value judgments, but judgement about something different from that pertaining to complexity. We have said elsewhere (Allen and Hoekstra, 2015; for instance) that things may exist in the world, but not as things. The “thingedness” comes from human decisions to put a boundary in place relative to a fluid experience. Complicatedness can take many forms, one of which might be about the number of parts to a structure. Ecologists fixate on the number of parts, and call it diversity, but there are many other ways to be complicated (e.g. elaboration of the outline). Number of parts might lead one to think that complicatedness is directly material. However, the number of parts is a decision of the observer, and so is tied to a concept before it is applied to observables. There are still abstractions underfoot. Complicatedness like complexity is a matter of human judgement, but the respective judgements are directed at different facets of observables from different levels of discourse (Fig. 2). In the end we are dealing with discourse, not materiality.

5. Conclusion As we argued above, complexity is about purpose of the whole, as it is captured in the constraints that relate the parts to each other and the whole. Degrees of freedom are lost as units become parts. Complexity pertains to the degrees of freedom that are taken away so the parts can function as such. It is often said that in emergence the whole is greater than the sum of the parts. Complexity can appear in that discourse. But it is also true that the sum of the parts is greater than the whole because the parts outside the constraints of the whole can do things they cannot do if constrained in the whole. Populations in isolation can grow when those under the constraints of a community may not. Complicatedness can appear in that second discourse about the parts recognized as separate. When George Box (Box and Draper, 1987) said, “All models are wrong, but some models are useful,” he spoke

of the arbitrary decisions in freezing bits of experience. Presumably what makes the models wrong is the way that human judgement is external relative to the things in question. Models are always for some purpose or another. The model’s purpose or usefulness is embodied in the questions that are asked of it. Consider the complexity of the brain. Allen once said in an Ecological Society of America (ESA) meeting evening session that the brain can either be complex or simple depending on the question asked. Others insisted the brain was in and of itself certainly complex. They wished to take a vote on it. There was no sense of irony that a vote is about as normative as it gets, and so has little “in and of itself” to it. Questions about the brain with regard to neurons and cognition invokes a complex system. But questions about the evolution of the mammalian brain from the reptilian brain raises only three parts, the hind- the mid- and the fore-brain. Furthermore there is only one trend, the fore-brain gets bigger. That invokes the brain as a simple system. The some of the discussants at the ESA meeting wished to invoke the real material brain as complex. Somehow that brain is supposed to deny a simple brain. But three parts and one trend does not accommodate complexity. We have carefully limited our discussion to epistemology, because only then can our discourse be consistent. We are not sure what the ontology of complexity could be. So what is the point of all we have said? Is it worth the effort? Yes, because so much time is invested in semantic argument in science, and particularly in ecology. The trouble is that the participants in semantic argument have little to let them know the problem of semantics exists. The disconnect between the epistemology of complexity and ontology is often ignored, and the problems are swept under the rug in muddled ecological discussions. Our arguments have been nuanced, and may appear esoteric. But we assert energetically that preempting a massive waste of time in semantics is an important and practical matter when complexity science is so expensive in these times of diminishing returns on effort.

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